Question: The sequence $2, 7, 12, a, b, 27$ is arithmetic. What is the value of $a + b$?
The common difference of the arithmetic sequence is $7-2=5$.  Therefore, the first six terms of the sequence are 2, 7, 12, 17, 22, and 27.  The sum of $a$ and $b$ is $17+22=\boxed{39}$.